Instead of redefining the target population, we can also replace the ACE with another parameter.[1]} First, point identification of the ACE can be abandoned in favor of partial identification, like bounds.[2]}, [3]}, [4]} However, point identification for other parameters may still be possible. Let \(g^*(\mathbf {Z})\)  indicate a general, investigator-specified plan that assigns actions based on \(\mathbf {Z}\) , where the ACE is a special case of \(g^*(\mathbf {Z})\) . Other plans, like \(g^*(\mathbf {Z})=0\)  if \(V=0,W=0\)  and \(g^*(\mathbf {Z})=1\)  otherwise, can also be considered. Specifically, this alternative \(g^*(\mathbf {Z})\)  avoids the deterministic positivity violation in \(S=1\) . For \(\mathbf {Z}\) -conditional plans generally, the deterministic positivity assumption is:
\(\Pr (A=a | \mathbf {Z}=\mathbf {z}) \ge \epsilon > 0 \text{ for } \mathbf {z} \text{ where } g^*(\mathbf {Z})=a\) 
